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Cochran Q test

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In statistics, the Q test a nonparametric statistical test used for identification and rejection of outliers. This test should be used sparingly and never more than once in a data set. To apply a Q test for bad data, arrange the data in order of increasing values and calculate Q as defined:

Q = Qgap/Qrange

Where Qgap is the absolute difference between the outlier in question and the closest number to it. If Qcalculated > Qtable then reject the questionable point.

TableEdit

Number of values:  3
4
5
6
7
8
9
10
Q90%:
0.941
0.765
0.642
0.560
0.507
0.468
0.437
0.412
Q95%:
0.970
0.829
0.710
0.625
0.568
0.526
0.493
0.466

ExampleEdit

For the data:

0.189, 0.169, 0.187, 0.183, 0.186, 0.182, 0.181, 0.184, 0.181, 0.177

Arranged in increasing order:

0.169, 0.177, 0.181, 0.181, 0.182, 0.183, 0.184, 0.186, 0.187, 0.189

Outlier is 0.169. Calculate Q:

Q=\frac{\mathrm{gap}}{\mathrm{range}}=\frac{(0.177-0.169)}{(0.189-0.169)}=0.400.

With 10 observations at 90% confidence, Qcalculated < Qtable. Therefore keep 0.169 at 90% confidence.

See alsoEdit

ReferencesEdit


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